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CAT Critical Reasoning Practice question with Solution 93

A survey of alumni of the class of 1960 at Aurora University yielded puzzling results. When asked to indicate their academic rank, half of the respondents reported that they were in the top quarter of the graduating class in 1960.

Which one of the following most helps account for the apparent contradiction above?

[A]. A disproportionately large number of high-ranking alumni responded to the survey.
[B]. Few, if any, respondents were mistaken about their class rank.
[C]. Not all the alumni who were actually in the top quarter responded to the survey.
[D]. Almost all of the alumni who graduated in 1960 responded to the survey.
[E]. Academic rank at Aurora University was based on a number of considerations in addition to average grades
Answer: A

How can 50 percent of the respondents be among the top 25 percent of the class? This only seems to be a contradiction: If the number of respondents was smaller than the total number of graduates, and if many of those who responded were students with high academic rank, then it’s quite possible that half of the respondents graduated in the top 25 percent of the class. The only “puzzle” here was if you didn’t see that the respondents could be a subset of the total set of graduates, or if you assumed that everyone in the class responded. (Then it’d be a puzzle, all right!—see (D), below.) Anyhow, (A) makes it all clear: The group of respondents included more than its share of people who graduated with high ranks.

(B) reinforces the accuracy of the numbers, without making it clearer how 50 percent of respondents fits into 25 percent of graduates.

(C) tells us that some of the 25 percent who graduated at the top of the class weren’t respondents, which makes it harder to see how 50 percent of the respondents came from the top 25 percent of the class.

(D) is even worse than (C). If the number of respondents roughly = the number of graduates, then we’d have more than 1/4 of the graduates saying that they were in the top 25th %ile of graduates. Rather than explaining an apparent discrepancy, (D) creates a real one.

(E) deals with the criteria for academic rank, which is outside the scope of the argument. We need help with the numbers, and (E) gives us no information that explains how 1/2 of respondents can be 1/4 of graduates.

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